CN106199670A - A kind of GNSS single-frequency single epoch attitude determination method based on Monte Carlo - Google Patents
A kind of GNSS single-frequency single epoch attitude determination method based on Monte Carlo Download PDFInfo
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- CN106199670A CN106199670A CN201610487545.9A CN201610487545A CN106199670A CN 106199670 A CN106199670 A CN 106199670A CN 201610487545 A CN201610487545 A CN 201610487545A CN 106199670 A CN106199670 A CN 106199670A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/53—Determining attitude
- G01S19/54—Determining attitude using carrier phase measurements; using long or short baseline interferometry
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/53—Determining attitude
- G01S19/54—Determining attitude using carrier phase measurements; using long or short baseline interferometry
- G01S19/55—Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
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Abstract
A kind of GNSS single-frequency single epoch attitude determination method based on Monte Carlo, its step is as follows: one: preparation: mainly provide border, linearizing station interspace double difference model;Two: set up multivariable GNSS attitude mode;Three: with the probability-distribution function of Monte Carlo sampling method structure fuzziness;Four: go out the candidate value of fuzziness by LAMBDA algorithm search;Five: calculate fuzziness optimum integer solution and determine attitude;Pass through above step, expectation and the covariance of fuzziness has been tried to achieve with monte carlo method, then use it for solving the resolving carrying out fuzziness in the LAMBDA method of fuzziness, decrease the amount of calculation calculating fuzziness, break away from the dependence to Pseudo range measurement, such that it is able to simple and efficient determination attitude, reduce the requirement to environmental condition.The present invention, during determining attitude, can quickly fix fuzziness, such that it is able to quickly determine attitude.
Description
Technical field
The present invention provides the single-frequency single epoch attitude determination method of a kind of GNSS based on Monte Carlo, and it relates to one
Plant GNSS single-frequency single epoch fuzziness based on Monte Carlo to fix and Attitude estimation method, i.e. a kind of to static or fortune
Mobile carrier utilize GNSS to carry out single-frequency single epoch carrier ambiguities that attitude determines is fixing and Attitude estimation method, belongs to navigation skill
Art field.
Background technology
GLONASS (GNSS, Global Navigation Satellite System) currently mainly includes
The global positioning system (GPS) of the U.S., Muscovite glonass system (GLONASS), the triones navigation system of China
And the Galileo system (Galileo) in Europe (BeiDou).GNSS system has in real time, high accuracy and whole world covering continuously etc.
Advantage, can be that surface car, naval vessel, aviation aircraft and low orbit satellite provide accurate time transmission, position and determine the navigation such as appearance
Service.In recent years, attitude based on GNSS determines that technology has obtained paying close attention to widely in navigation field.By on carrier platform
At least three GNSS receiver is installed, builds single poor or double difference observational equation, it is possible to obtain the complete attitude information of carrier.GNSS
Attitude determines have zero shift, low cost, the advantage such as low in energy consumption, can realize existing attitude determination system well substituting, perfect
Or supplement.
The basic observation of GNSS system comprises pseudorange and carrier wave two kinds, and the observation noise of the two is respectively at decimetre and millimeter
Level.High-precision GNSS attitude determines and relies primarily on carrier signal, especially for the fortune of small-medium size (meter level or decimeter grade)
Mobile carrier, the most middle-size and small-size vehicle, unmanned plane, sounding rocket, satellite etc., it is necessary to by carrier signal.But, carrier signal is deposited
In integer ambiguity problem.Therefore, fixed carrier phase integer ambiguity the most fast and accurately, is to realize high-precision GNSS appearance
Core that state determines and key.According to whether utilizing the relative motion between carrier and GNSS satellite during ambiguity resolution believe
Breath, can determine attitude that Ambiguity Solution Methods is divided into method many epoch and single epoch method two kinds.Many epoch, method was also known as the method for movement,
Its ultimate principle is to utilize the accumulated time of observation information to obtain fuzziness float-solution and covariance matrix, thus obtains fixing whole
Number solves.Many epoch, method was easily subject to carrier signal losing lock and the impact of fuzziness cycle slip, was unfavorable in complicated navigational environment
(signal cover, high dynamic flying etc.) uses.By contrast, single epoch method can not be affected by signal losing lock and cycle slip.And
And, the fixed speed of single epoch method itself to be faster than method many epoch.Realize single epoch fuzziness to fix, several way can be taked
Footpath, the such as combination of traversal search, multiple-frequency signal and multi-receiver length-short baseline configuration etc..Appearance is determined for low cost single-frequency GNSS,
Search method is optimum selection.Wherein, (least square fuzziness decorrelation adjusts LAMBDA method, Least squares
AMBiguity Decorrelation Adjustment) it is a kind of the highest, the most widely used method of current efficiency.LAMBDA side
A kind of integer least square search method of method, makes the degree of correlation of the fuzziness of different passage drop to by transform
Minimum, still retain its integer characteristic simultaneously, therefore there is higher search efficiency and accuracy.But, apply LAMBDA method
Fixing fuzziness needs to utilize pseudorange and carrier wave to measure simultaneously.The Main Function of pseudorange is the hunting zone reducing fuzziness, and
It not that attitude algorithm is directly provided.When pseudorange noise is less (5~30cm), LAMBDA method can realize 100% fuzzy
Degree is fixed into power;As pseudorange noise excessive (> 50cm) or multipath error in the presence of, performance can decline therewith.
The present invention proposes a kind of GNSS single-frequency single epoch mould based on Monte Carlo on the basis of LAMBDA method
The fixing method determined with attitude of paste degree.The method, from the angle of fuzziness probability distribution, utilizes previously known many days
The search volume of fuzziness is defined by line geometry distributed intelligence, thus breaks away from the dependence to pseudo range signals, therefore can use
In high pseudorange noise (low-end receivers, weak signal environment etc.) and high multi-path environment (avenue, support shapes are irregular)
Attitude determine.The method is suitable for use with short baseline and ultra-short baseline determines middle-size and small-size (static or motion) carrier of appearance.
Summary of the invention
(1) goal of the invention: the present invention fixes based on fuzziness method by LAMBDA, for short baseline and ultra-short baseline
Attitude determines problem, it is proposed that a kind of GNSS single-frequency single epoch fuzziness based on Monte Carlo is fixed and Attitude estimation side
Method.
(2) technical scheme
A kind of GNSS single-frequency single epoch attitude determination method based on Monte Carlo of the present invention, its step is as follows:
Step one: preparation
First, m+1 the receiver carrier observations amount to n+1 GNSS satellite is given to departures border-interspace double difference observation
Lienarized equation is as follows:
In formula (1), Φ is n × m rank matrix of the carrier wave double difference composition of m bar basic lineal vector, each column vector table
Show n the double difference that a baseline is corresponding;B is m bar the unknown basic lineal vector coordinate figure group under GNSS reference frame
3 × m rank the matrix become;G is from the double difference unit vector of satellite to receiver direction expression group under GNSS reference frame
Rank, n × 3 matrix that becomes (owing to the spacing of each secondary receiver is the least, and each secondary receiver of satellite distance is far, so here
Think that same satellite is identical to the unit vector in any one secondary receiver direction);λ is carrier wavelength;Z is double difference complete cycle mould
N × m rank matrix of paste degree composition, each column vector represents n the double difference integer ambiguity that a baseline is corresponding;V observation noise
N × m rank matrix of composition;Symbol vec () represents presses row sequence number order from small to large successively from upper matrix column vector
It is rearranged into string under to, forms new column vector;Q is the covariance matrix of vec (V);Taking Q is:
Wherein σ is the standard deviation of carrier noise;SymbolRepresent Kronecker product;
Monte Carlo sampling method:Represent probability-distribution function pxThe random measurement of (x),It is sample point,It is the weight that each point is corresponding, andNsIt is sampling number of times, then probability-distribution function pxX () can approximate representation
For
Wherein, δ () represents Dirac delta function;
Step 2: set up multivariable GNSS attitude mode
Definition local coordinate: initial point is in main receiver position, and x-axis is along Article 1 base direction, and y-axis is at Article 1 base
The plane that line and Article 2 baseline determine is interior and is perpendicular to x-axis, and z-axis direction is determined by the right-hand rule;M bar basic lineal vector is at this
Representing it is known that the 3 × m coordinates matrix F being then made up of m bar basic lineal vector is as follows in ground coordinate system:
Wherein, in F, each column vector represents the expression under local coordinate of the basic lineal vector, it may be assumed that at local coordinate system
Under system, the coordinate of secondary receiver 1 is (f11, 0,0), the coordinate of secondary receiver 2 is (f21,f22, 0), the coordinate of secondary receiver 3 is
(f31,f32,f33), the coordinate of secondary receiver m is (fm1,fm2,fm3), wherein the implication of each coordinate figure is shown in Figure of description
Fig. 2;
R is made to represent the coordinate transfer matrix being tied to GNSS reference frame from local coordinate system, then
B=RF (5)
Substituted into formula (1) and i.e. be can get multivariable GNSS attitude mode:
Wherein, 3 rank normal orthogonal square formations R and double difference fuzziness matrix are unknown quantity;By the quaternary number table of the parameter in R
Show, then (6) formula can be written as:
Wherein, q=(q0,q4)T, q0=(q1,q2,q3)T, and meet qTQ=1,
Q is unknown quantity;
Upper described, described " setting up multivariable GNSS attitude mode ", its process set up is by (4) formula and (5)
Formula substitutes into (1) formula and obtains (6) formula, then (8) formula substitution (6) formula is obtained (7) formula, and (7) formula is the multivariate GNSS appearance of foundation
States model;
Step 3: the probability-distribution function of Monte Carlo sampling method structure fuzziness
According to (7) formula, double difference fuzziness can be expressed as:
Observation noise defer to average be 0 covariance be the normal distribution of Q;The probability-distribution function of vec (V) is:
If it is known that quaternary number q has upper bound quWith lower bound ql, according to priori attitude information, q defers to and is uniformly distributed:
Wherein,
According to qTQ=1, can obtain
Further,
Wherein,It is qlFirst three component,It is quFirst three component.In the case of lacking priori attitude information,
Desirable ql=[1,1,1]T, qu=[1,1,1]T;According to probability-distribution function pq(q) and pvec(V)V () carries out N to q and vsSub-sampling
The weight that sample point is corresponding every time is
The sample point of fuzziness can be drawn according to (9) formulaThen
The expectation of fuzziness and covariance are
Here the expectation drawn and variance are by the LAMBDA algorithm being used for step 4;
Upper described, described " probability-distribution function of structure fuzziness ", refers to first according to pose transformation matrix R (q)
In quaternary number element q and the probability-distribution function of noise q and noise are sampled respectively, sampling result obtain fuzziness
Sample, so can obtain the probability-distribution function of fuzziness according to monte carlo method;
Step 4: LAMBDA algorithm search goes out the candidate value of fuzziness
Owing to LAMBDA algorithm is existing ready-made method, do not elaborate;Can be searched by LAMBDA algorithm
Rope goes out NcThe candidate value of individual fuzziness
Step 5: calculate fuzziness optimum integer solution and determine attitude
Attitude matrix corresponding to each candidate value can be calculated to obtain according to (9) formula by the candidate value of fuzziness
X+The pseudoinverse of representing matrix X.The wherein candidate value of quaternary numberCan be obtained by following formula
Wherein { Rij, i, j=1,2,3} are the elements of matrix R;Then final integer solution and the attitude matrix of fuzziness is
Wherein, the candidate value of fuzziness " the LAMBDA algorithm search go out " described in step 4, process of its search is such as
Under:
First do not consider that the integer of fuzziness limits, directly go out the float-solution of fuzziness with least square solution, obtaining above
The covariance matrix structural transform matrix Z gone out, uses Z integer transition matrix fuzziness and covariance matrix to be changed, enters
Row searching for integer cycle, tries to achieve integer solution and the covariance matrix thereof of fuzziness, then to the fuzziness tried to achieve and covariance square
Battle array carries out Z inverse transformation, obtains integer solution and the covariance matrix thereof of fuzziness;
By above step, try to achieve expectation and the covariance of fuzziness with monte carlo method, then used it for asking
The LAMBDA method of ambiguity solution degree carries out the resolving of fuzziness, decreases the amount of calculation calculating fuzziness, broken away from pseudorange
The dependence of measurement amount, such that it is able to simple and efficient determination attitude, reduces the requirement to environmental condition.
(3) advantage
The advantage of the single-frequency single epoch attitude determination method of a kind of based on Monte Carlo the GNSS that the present invention provides
It is:
1. for the attitude of baseline, the present invention determines that the resolving with fuzziness need not the auxiliary of Pseudo range measurement, well
It is applicable at high pseudo range measurement noise, under the conditions of multipath.
2. the present invention is during determining attitude, and the amount of calculation calculating fuzziness variance is little, thus reduces overall calculating
Amount.
3. the present invention is during determining attitude, can quickly fix fuzziness, such that it is able to quickly determine attitude.
Accompanying drawing explanation
Fig. 1 is the method for the invention flow chart.
Fig. 2 is the schematic diagram of each basic lineal vector under local coordinate.
Detailed description of the invention
The single-frequency single epoch attitude determination method of a kind of GNSS based on Monte Carlo of the present invention, as shown in Figure 1, its
It is embodied as step as follows:
Step one: provide linearizing interspace-border double difference model of standing
Border, the station-interspace double difference of the carrier observations amount of n+1 GNSS satellite is observed lienarized equation such as by m+1 receiver
Shown in lower:
In formula (23), Φ is n × m rank matrix of the carrier wave double difference composition of m bar basic lineal vector, each column vector table
Show n the double difference that a baseline is corresponding;B is m bar the unknown basic lineal vector coordinate figure group under GNSS reference frame
3 × m rank the matrix become;G is from the double difference unit vector of satellite to receiver direction expression group under GNSS reference frame
Rank, n × 3 matrix that becomes (owing to the spacing of each secondary receiver is the least, and each secondary receiver of satellite distance is far, so here
Think that same satellite is identical to the unit vector in any one secondary receiver direction);λ is carrier wavelength;Z is double difference complete cycle mould
N × m rank matrix of paste degree composition, each column vector represents n the double difference integer ambiguity that a baseline is corresponding;V observation noise
N × m rank matrix of composition;Symbol vec () represents presses row sequence number order from small to large successively from upper matrix column vector
It is rearranged into string under to, forms new column vector;Q is the covariance matrix of vec (V).Taking Q is:
Wherein σ is the standard deviation of carrier noise;SymbolRepresent Kronecker product.
Step 2: set up multivariable GNSS attitude mode
Definition local coordinate: initial point is in main receiver position, and x-axis is along Article 1 base direction, and y-axis is at Article 1 base
The plane that line and Article 2 baseline determine is interior and is perpendicular to x-axis, and z-axis direction is determined by the right-hand rule.M bar basic lineal vector is at this
Representing it is known that the 3 × m coordinates matrix F being then made up of m bar basic lineal vector is as follows in ground coordinate system:
Wherein, in F, each column vector represents the expression under local coordinate of the basic lineal vector, wherein each coordinate figure
Implication see accompanying drawing 2.
R is made to represent the coordinate transfer matrix being tied to GNSS reference frame from local coordinate system, then B=RF.So, multivariate
GNSS attitude mode can be obtained by formula (23):
Wherein, 3 rank normal orthogonal square formations R and double difference fuzziness matrix Z are unknown quantity.By the quaternary number table of the parameter in R
Show, then (26) formula can be written as:
Wherein, q=(q0,q4)T, q0=(q1,q2,q3)T, and meet qTQ=1,
Q is unknown quantity.
According to (27) formula, double difference fuzziness can be expressed as:
Step 3: the probability-distribution function of Monte Carlo sampling method structure fuzziness
Observation noise defer to average be 0 covariance be the normal distribution of Q, then the probability-distribution function of vec (V) is:
If it is known that quaternary number q has upper bound quWith lower bound ql, according to priori attitude information, q defers to and is uniformly distributed:
Wherein,
According to qTQ=1, can obtain
Further,
Wherein,It is qlFirst three component,It is quFirst three component.In the case of lacking priori attitude information,
Desirable ql=[1,1,1]T, qu=[1,1,1]T。
According to probability-distribution function pq(q) and pvec(V)V () carries out N to q and vsSub-sampling
The weight that sample point is corresponding every time is
The sample point of fuzziness can be drawn according to (29) formulaThen
The expectation of fuzziness and covariance are
Here the expectation drawn and variance are by the LAMBDA algorithm being used for step 4.
Step 4: LAMBDA algorithm search goes out the candidate value of fuzziness
Owing to LAMBDA algorithm is existing ready-made method, do not elaborate.Can be searched by LAMBDA algorithm
Rope goes out NcThe candidate value of individual fuzziness
Step 5: calculate attitude matrix corresponding to each fuzziness candidate value and filter out optimal solution
Attitude matrix corresponding to each candidate value can be calculated to obtain according to (27) formula by the candidate value of fuzziness
Symbol X+The pseudoinverse of representing matrix X.The candidate value of its quaternary numberCan be obtained by following formula
Wherein { Rij, i, j=1,2,3} are the elements of matrix R.
The final integer solution of fuzziness and attitude matrix are
Claims (2)
1. a GNSS single-frequency single epoch attitude determination method based on Monte Carlo, it is characterised in that: its step is as follows:
Step one: preparation
First, m+1 the receiver carrier observations amount to n+1 GNSS satellite is given linear to departures border-interspace double difference observation
Change equation as follows:
In formula (1), Φ is n × m rank matrix of the carrier wave double difference composition of m bar basic lineal vector, and each column vector represents one
N the double difference that bar baseline is corresponding;B is the 3 of m bar the unknown basic lineal vector coordinate figure composition under GNSS reference frame
× m rank matrix;G be from the double difference unit vector of satellite to receiver direction under GNSS reference frame represent composition n
× 3 rank matrixes;λ is carrier wavelength;Z is n × m rank matrix of double difference integer ambiguity composition, and each column vector represents a base
N the double difference integer ambiguity that line is corresponding;N × m rank matrix of V observation noise composition;Symbol vec () represents matrix column
Vector is rearranged into string the most from top to bottom by row sequence number order from small to large, forms new column vector;Q is vec (V)
Covariance matrix;Taking Q is:
Wherein σ is the standard deviation of carrier noise;SymbolRepresent Kronecker product;
Monte Carlo sampling method:Represent probability-distribution function pxThe random measurement of (x),It is sample point,
It is the weight that each point is corresponding, andNsIt is sampling number of times, then probability-distribution function pxX () approximate representation is
Wherein, δ () represents Dirac delta function;
Step 2: set up multivariable GNSS attitude mode
Definition local coordinate: initial point in main receiver position, x-axis along Article 1 base direction, y-axis at Article 1 baseline and
The plane that Article 2 baseline determines is interior and is perpendicular to x-axis, and z-axis direction is determined by the right-hand rule;M bar basic lineal vector is sat in this locality
Representing it is known that the 3 × m coordinates matrix F being then made up of m bar basic lineal vector is as follows in mark system:
Wherein, in F, each column vector represents the expression under local coordinate of the basic lineal vector, it may be assumed that under local coordinate,
The coordinate of secondary receiver 1 is (f11, 0,0), the coordinate of secondary receiver 2 is (f21,f22, 0), the coordinate of secondary receiver 3 is (f31,
f32,f33), the coordinate of secondary receiver m is (fm1,fm2,fm3);
R is made to represent the coordinate transfer matrix being tied to GNSS reference frame from local coordinate system, then
B=RF (5)
Substituted into formula (1) and i.e. obtained multivariable GNSS attitude mode:
Wherein, 3 rank normal orthogonal square formations R and double difference fuzziness matrix are unknown quantity;Parameter quaternary number in R is represented, then
(6) formula is written as:
Wherein, q=(q0,q4)T, q0=(q1,q2,q3)T, and meet qTQ=1,
Q is unknown quantity;
Step 3: the probability-distribution function of Monte Carlo sampling method structure fuzziness
According to (7) formula, double difference fuzziness is expressed as:
Observation noise defer to average be 0 covariance be the normal distribution of Q;The probability-distribution function of vec (V) is:
If it is known that quaternary number q has upper bound quWith lower bound ql, according to priori attitude information, q defers to and is uniformly distributed:
Wherein,
According to qTQ=1,
Further,
Wherein,It is qlFirst three component,It is quFirst three component;In the case of lacking priori attitude information, take ql
=[1,1,1]T, qu=[1,1,1]T;According to probability-distribution function pq(q) and pvec(V)V () carries out N to q and vsSub-sampling
The weight that sample point is corresponding every time is
The sample point of fuzziness is drawn according to (9) formulaThen
The expectation of fuzziness and covariance are
Here the expectation drawn and variance are by the LAMBDA algorithm being used for step 4;
Step 4: LAMBDA algorithm search goes out the candidate value of fuzziness
Owing to LAMBDA algorithm is existing ready-made method, do not elaborate;N can be searched out by LAMBDA algorithmcIndividual
The candidate value of fuzziness
Step 5: calculate fuzziness optimum integer solution and determine attitude
Attitude matrix corresponding to each candidate value is calculated to obtain according to (9) formula by the candidate value of fuzziness
X+The pseudoinverse of representing matrix X;The wherein candidate value of quaternary numberObtained by following formula
Wherein { Rij, i, j=1,2,3} are the elements of matrix R;Then final integer solution and the attitude matrix of fuzziness is
By above step, try to achieve expectation and the covariance of fuzziness with monte carlo method, then used it for solving mould
The LAMBDA method of paste degree carries out the resolving of fuzziness, decreases the amount of calculation calculating fuzziness, broken away from pseudo range measurement
The dependence of amount, it is thus possible to simple and efficient determination attitude, reduces the requirement to environmental condition.
A kind of GNSS single-frequency single epoch attitude determination method based on Monte Carlo the most according to claim 1, its
Being characterised by: the candidate value of fuzziness " the LAMBDA algorithm search go out " described in step 4, process of its search is as follows:
First do not consider that the integer of fuzziness limits, directly go out the float-solution of fuzziness with least square solution, the association side drawn
Difference matrix construction transition matrix Z, uses Z integer transition matrix fuzziness and covariance matrix to be changed, carries out complete cycle mould
Paste degree is searched for, and tries to achieve integer solution and the covariance matrix thereof of fuzziness, then it is inverse that the fuzziness tried to achieve and covariance matrix are carried out Z
Conversion, obtains integer solution and the covariance matrix thereof of fuzziness.
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CN109932735A (en) * | 2019-03-25 | 2019-06-25 | 中国铁路设计集团有限公司 | The localization method of the short baseline single-frequency simple epoch solution of Beidou |
CN110133702A (en) * | 2019-05-13 | 2019-08-16 | 桂林电子科技大学 | A kind of attitude measurement method and equipment based on orthogonal transformation |
CN110133702B (en) * | 2019-05-13 | 2022-12-27 | 桂林电子科技大学 | Attitude measurement method and equipment based on orthogonal transformation |
CN115184895A (en) * | 2022-09-07 | 2022-10-14 | 北京海兰信数据科技股份有限公司 | Static target identification method and system based on navigation radar |
CN115877431A (en) * | 2023-01-04 | 2023-03-31 | 中国民航大学 | Array antenna non-whole-cycle fuzzy strategy based low-operand direction-finding device and method |
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